Theorem mulcomi 8163

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8139	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1395   e. wcel 2200  (class class class)co 6007   CCcc 8008   x. cmul 8015

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8111

This theorem is referenced by:  mulcomli  8164  8th4div3  9341  numma2c  9634  nummul2c  9638  9t11e99  9718  binom2i  10882  fac3  10966  tanval2ap  12239  pockthi  12896  decsplit1  12966  decsplit  12967  sincosq4sgn  15518  2logb9irrALT  15663  2lgsoddprmlem2  15800  2lgsoddprmlem3d  15804